Basic Mathematical Investigations in Electromagnetic Wave Theory Final Report
Basic Mathematical Investigations in Electromagnetic Wave Theory Final Report
Joseph B Keller
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The solution u of a wave propagation problem for the medium a depends upon a. Therefore it is denoted by u(a) and with it is associated the probability distribution p(a). This makes u(a) a random wave. Then the mean value of any functional F[u] is denoted by and is defined by (1) = F[u(a)]p(a)da. It is assumed that certain statistical properties of the wave in the 30 random medium will correspond to properties of the wave in a given com- plex medium, provided that the random medium is chosen ...appropriately to model that medium. In a general way the problem and the basic methods employed in reports EM-208, 210 and 231 may be formulated as follows. Let it be assumed that in the medium a, the state of the system u(a) = u(x, t;a), a vector function of space and time, (2) L(a)u = g where L(a) is a linear operator depending on a, and g is a given non- random function. If L(a) is invertible, as we assume it to be for almost all a, we may write the solution of (1) as u(a) = L (a)g.
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